Blender 2.8 Beta will not run on Linux Mint.
sometimes blender quits before being even fully loaded or just not responds and for this behaviour You may try to access the folder where blender executable file is and run './blender' or 'sudo ./blender' or if You have blender installed as package just run straight these commands without searching for path to blender exec file. If there's an issue it will be printed in terminal. As an example, one instance of Blender not working in Linux Mint was an unsupported video card, or your computer not having the latest installment of (OpenGL 3.3) installed.